The present work describes some aspects of the diagnostic problem solving architecture of ADAPTER, a multi-modal reasoning system combining Case- Based Reasoning (CBR) and Model-Based Reasoning (MBR). In particular, some issues concerning the performance of such a combined architecture are discussed, with particular attention to the problem of maintaining under control the growth of the case memory. In fact, an over-sized case memory is the main responsible for the arising of the utility problem in ADAPTER. We identified such a responsibility through a set of experiments concerning the average behavior of the system with respect to a given domain. As a consequence, we propose two learning strategies regarding the addition and replacement of cases in memory. Experimental results are quite encouraging and suggest that the adoption of such strategies can greatly mitigate the over-sizing of the case memory.